The invention is based on an apparatus for closing containers, such as bottles, as defined hereinafter. In an apparatus of this kind, known for instance from DE-OS 39 08 582, the end segment of the jacket of the capsule, pressed onto the top of the bottle by a male die, is crimped around the neck of the bottle continuously by rotation of the bottle with the capsule against a fixed disk -with point-type contact. In another, one or more crimping rollers circle around the capsule and by rolling along it again gradually crimp the end portion of the capsule jacket around the top of the bottle, again with point-type contact. A disadvantage of this known apparatus is that the engagement of this crimping tool produces abrasion in the course of rotation; such abrasion must be avoided, particularly when packaging pharmaceuticals. An apparatus that meets the demands for cleanliness of the surrounding atmosphere in the field of pharmaceuticals is therefore desirable.